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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Circular coloring ： ウィキペディア英語版 Circular coloring In graph theory, circular coloring may be viewed as a refinement of usual graph coloring. The ''circular chromatic number'' of a graph $G$, denoted $\backslash chi\_c(G)$ can be given by any of the following definitions, all of which are equivalent (for finite graphs). #$\backslash chi\_c(G)$ is the infimum over all real numbers $r$ so that there exists a map from $V(G)$ to a circle of circumference 1 with the property that any two adjacent vertices map to points at distance $\backslash ge\; \backslash frac$ along this circle. #$\backslash chi\_c(G)$ is the infimum over all rational numbers $\backslash frac$ so that there exists a map from $V(G)$ to the cyclic group $/n$ with the property that adjacent vertices map to elements at distance $\backslash ge\; k$ apart. #In an oriented graph, declare the ''imbalance'' of a cycle $C$ to be $|E(C)|$ divided by the minimum of the number of edges directed clockwise and the number of edges directed counterclockwise. Define the ''imbalance'' of the oriented graph to be the maximum imbalance of a cycle. Now, $\backslash chi\_c(G)$ is the minimum imbalance of an orientation of $G$. It is relatively easy to see that $\backslash chi\_c(G)\; \backslash le\; \backslash chi(G)$ (especially using 1. or 2.), but in fact $\backslash lceil\; \backslash chi\_c(G)\; \backslash rceil\; =\; \backslash chi(G)$. It is in this sense that we view circular chromatic number as a refinement of the usual chromatic number. Circular coloring was originally defined by , who called it "star coloring". Coloring is dual to the subject of nowhere-zero flows and indeed, circular coloring has a natural dual notion: circular flows. ==See also== *Rank coloring 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Circular coloring」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.